The previous chapter presented a model for the lethality of hunting bullets which is one of the limiting factors in long range hunting. This chapter focuses on the other major constraint which is accuracy. Once you’ve determined the approximate maximum lethal range of your selected rifle and bullet, it’s important to understand the uncertainties involved which may cause you to miss your aimpoint. Accuracy is obviously a very important factor in long range hunting. Not only do you have to hit the animal, but you have to hit it in a vital area which is a small percentage of the animal’s total size. If you are accurate enough and can reliably place shots within the small vital area of your target, you can effectively increase the lethal range with superior shot placement

This chapter will focus on a general model that will attempt to quantify the probability of a hit against a certain target given unique field variables. For example, if you know your rifle’s inherent precision (grouping ability), muzzle velocity variation, wind uncertainty, range to target and target size, you should be able to estimate the probability of successfully hitting the target on the first shot. Like the previous chapter on lethality, the goal here is not to give hard numbers that are 100% accurate. Rather the goal is to reveal the underlying trends and provide some realistic guidance to the decision making process.

Accounting for uncertainty
Long range shooting has many variables. Most of the variables can be measured and accounted for. These are known as deterministic variables. Examples of deterministic variables are: gravity drop, range, atmospherics, rifle cant (tilt), and spin drift. Every deterministic variable can be quantified and corrected for. If all variables were deterministic, shooters would only be limited by their rifles inherent precision (grouping ability). For example, if a rifle was capable of 10” groups at 1000 yards, you could expect to be able to reliably hit a 10” target at 1000 yards, etc. Long range shooters know that in reality, you cannot count on perfect shot placement. The reason why you can’t is because of the non-deterministic variables involved in long range shooting. Non-deterministic variables are those variables that cannot be measured precisely or calculated for each shot.

The two biggest non-deterministic variables remaining in long range shooting are wind determination and muzzle velocity variation. Furthermore, there are the effects introduced by firing from a cold bore.

The following analysis will proceed with the assumption that the shooter has measured and accounted for all of the deterministic variables, and will focus on the effects of the non-deterministic variables.

Figure 15.1 illustrates how the non-deterministic effects of muzzle velocity variation and wind deflection combine to shape a likely impact zone for a given set of non-deterministic variables. The goal is to determine the size and shape of the impact zone under the influence of some non-deterministic variables.

Step 1: Establish the baseline.
This is the inherent precision ability of the rifle and can be determined by averaging groups at short range. It’s important to be honest with this part. The goal is to represent the average grouping potential of the rifle, not the best ever 3 shot group. A good way to establish the baseline is to average 5 groups of 5 shots each. This will give a good representation of the rifles inherent precision. Contrary to the belief of many gun writers and shooters, a single 3-shot group is worthless for determining the grouping potential of any rifle.

For this example, we’ll consider a 30-06 rifle shooting 185 grain bullets at an average muzzle velocity of 2850 fps. The rifle will be modeled as being capable of 1” groups at 100 yards on average. For this current analysis, we’ll consider the impact zone at 500 yards. According to the principles of bullet dispersion given in Chapter 11, we can extrapolate the group size from 100 yards to 500 yards based on the bullets time of flight. The bullets time of flight at 100 yards is 0.1084 seconds, and at 500 yards, it’s 0.6154 seconds. Since the rifle is capable of grouping into 1 inch at 100 yards, we can expect the dispersion to produce a 500 yard group of: 1 inch times 0.6154/0.1084 = 5.7 inches minimum.

The next piece of information we need is the extreme spread of muzzle velocity variation for the load under consideration. The extreme spread (ES) should be mesured for as many shots as possible; at least 10 shots should make up the sample. Alternatively, you can use 4 times the standard deviation as a representation of the muzzle velocity extreme spread (+/- 2 standard deviations represents 95% confidence limits). This statistical data gathered on the muzzle velocity will be used to characterize the uncertainty of this non-deterministic variable so that we can correlate it to an expected vertical dispersion. For this example, we’ll use an extreme spread of 60 fps in muzzle velocity. That would roughly correlate to a standard deviation of about 15 fps.

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The final piece of information we need for step 1 is the uncertainty of the crosswind, similar to the target shooting analysis in the previous section. This is a difficult variable to nail down because it’s purely an estimate of your ability to judge the average crosswind speed between you and the target. How accurately this can be done depends on the indicators that are available, the complexity of the wind patterns present, and the accuracy of the individual’s estimations. You can get an idea of how accurate your wind estimation is by taking a wind meter into the field, guessing at the wind speed, and seeing how close you come to the measured wind speed. This exercise will also serve as a learning experience, allowing you to calibrate your observations into accurate wind speeds. You will need to make a guess as to what your ability is to estimate crosswind speed in mph. For this example, we’ll say the shooter is capable of estimating crosswind within +/- 2 mph.

So the raw parameters we’ll be using to create the impact zone analysis at 500 yards are:
• Rifle capable of averaging 1” groups at 100 yards: extrapolates to 5.7 inches minimum at 500 yards.
• 60 fps extreme spread in muzzle velocity
• +/- 2 mph uncertainty in crosswind speed

The rifle’s inherent precision and the extreme spread of muzzle velocity can be considered relatively constant values whereas the uncertainty in wind speed is something that could be different for each shot.